OEMs (like GE, and probably Hitachi) publish documents with formulae and procedures for this very purpose.
The GE publication number, if I recall correctly, is GTS-111D. (I think the "D" refers to a revision designation; later alphabetic characters are newer revisions.) It seems GE is now making most of their turbine publications available online; try using your preferred World Wide Web search engine to look for GTS-111, or GTS-111D. The name of this publication is 'Estimating Gas Turbine Performance.'
For the most accurate estimations, though, you will need the various OEM Correction Curves (for ambient temperature, humidity, ambient pressure, etc.), which are usually provided by the OEM in the Operations & Service Manuals.
Hope this helps!